Wind power is considered one of the cleanest, most environmentally friendly energy sources presently available, and wind turbines have gained increased attention in this regard. A modern wind turbine typically includes a tower, a generator, a gearbox, a nacelle, and a rotor having one or more rotor blades. In many wind turbines, the rotor is attached to the nacelle and is coupled to the generator through the gearbox. The rotor and the gearbox are mounted on a bedplate support frame located within the nacelle. More specifically, in many instances, the gearbox is mounted to the bedplate via one or more torque supports or arms. The rotor blades capture kinetic energy of wind using known airfoil principles. The rotor blades transmit the kinetic energy in the form of rotational energy so as to turn a shaft coupling the rotor blades to a gearbox, or if a gearbox is not used, directly to a generator shaft of the generator. The gearbox may be used to step up the inherently low rotational speed of the turbine rotor for the generator to efficiently convert mechanical energy to electrical energy, which is provided to a utility grid.
Transmission of wind energy from remote locations to load centers or to main transmission backbones necessitates long transmission lines. Series capacitors are a proven and economical transmission solution to address system strength, grid stability, and voltage profile issues of long transmission lines. In some instances, wind turbine generators can be susceptible to sub-synchronous interaction (SSI) problems when the generator is connected to the grid through series-compensated transmission lines.
More specifically, wind turbines can interact with the grid resonances created by the series capacitor compensation, thereby causing wind turbine damage and/or misoperation if such interactions are not addressed. Further, wind generators react to grid transients according to their physical characteristics and control logic. When reacting to the sub-synchronous currents caused by series resonances in the grid, such reactions can affect the damping of the resonance. The phenomenon has been termed sub-synchronous interaction (SSI). SSI is benign in many cases, but in other cases, can lead to an electrical instability. When unstable, the sub-synchronous currents and voltages grow until a nonlinear event occurs.
One commonly used method for studying sub-synchronous interaction is frequency scanning analysis. A typical frequency scanning analysis includes establishing a steady state operating condition of the system under test, injecting a current (or voltage) perturbation signal to the steady state system, subtracting the perturbed system voltage and current by their steady state quantities to acquire the small signal delta change, performing Fast Fourier Transform (FFT), calculating the phasor value at the testing frequency, and calculating the system impedance. The steps may be repeated at other frequencies in the range of interest.
In addition, as shown in FIG. 1, the frequency scanning analysis treats the wind turbine generator 12 and the grid network 14 of the circuit 10 as two separate sub-systems. When the two sub-systems 12, 14 are connected together, the outcome is equivalent to summing their respective impedances. As such, a potential instability is indicated by a negative resistance at a resonance frequency (i.e. zero reactance). For example, as shown in FIG. 2, corresponding graphs of resistance versus frequency and reactance versus frequency, respectively, for the circuit 10 are illustrated. More specifically, two resonance frequencies 15, 17 (e.g. at about 10 Hz and about 51 Hz) are identified from the frequency impedance plots generated by the circuit 10. As shown, both resonance frequencies 15, 17 have negative damping as the associated resistances are negative, thereby indicating a potential instability of the system.
Although the above mentioned frequency analysis has been widely used for SSI evaluation, the results of such testing can be misleading due to the deficiencies in the method. For example, one such deficiency is the coupling frequencies effect as illustrated in FIGS. 3-5. More specifically, FIG. 3 illustrates a block diagram of a simplified control function that converts a three phase alternating-current (a-c) quantity (e.g. Xabc) into a direct quadrature (d-q) rotating coordinate, multiplies the d-q quantity by two gains (Kd and Kq) separately, and then reversely converts the result back into an a-c quantity (e.g. Yabc). A d-q transformation generally refers to a mathematical transformation that rotates the reference frame of three-phase systems in an effort to simplify the analysis of three-phase circuits. The input Xabc and the output Yabc can be voltage, current, or combinations thereof. As shown in FIGS. 4 and 5, two tests are run with different values of Kd and Kq using the control function. The ABC-to-DQ and the DQ-to-ABC transformations are based on the fundamental frequency, e.g. 60 Hz. FIG. 4 illustrates a comparison of the input and output in both the time domain and frequency spectrum from a first test, e.g. when Kd=Kq=1.0. As shown, the output equals to the input. In a second test, as shown in FIG. 5, Kd is different from Kq (i.e. the control becomes asymmetric) and the resulting output Yabc contains an additional frequency component 16 that is not in the input.
As shown in FIG. 6, a graph illustrating the effect of the coupling frequencies effect described above is illustrated. As shown, the graph compares the impedance calculated from the two grid conditions. If there is no coupling frequencies effect, the calculation results in the same generator impedance for both conditions such that the curves should overlap. The distinction between the two curves of FIG. 6, however, demonstrates the impact of coupling frequencies. In addition, the resulting frequency impedances of the generator from the two grid conditions render opposite indications to the SSI stability of the system. For example, when the grid connection is stiffer (curve 18), the generator resistance is positive over the whole sub-synchronous frequency range and therefore indicates no SSI instability. In contrast, when the grid connection is weaker (curve 20), the generator resistance is negative in sub-synchronous frequency range, thereby raising a concern of potential SSI instability. As such, the coupling frequencies effect complicates SSI evaluation for wind turbine generators. Further, the coupling frequencies effect contributes to the difficulty of system design as trying to design a stable system for the infinite number of grid scenarios is almost impossible.
In view of the aforementioned, a system and method that improves sub-synchronous interaction (SSI) damping of a wind turbine generator by utilizing symmetric control design would be advantageous.